1 Introduction
2 Background
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Surface finish instead of roughness
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Dimensional and geometric accuracy instead of deviations or errors
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Process speed instead of PT.
Performance measures Process parameters | Surface finish | Dimensional accuracy | Geometric accuracy | Process speed | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
↑ | - | ↓ | ↑ | - | ↓ | ↑ | - | ↓ | ↑ | - | ↓ | |
Layer thickness (LT) | [13] [14] | [15] [16] [27] [29] [30] [32] [38] [44] [46] [50] [53] [55] [56] [57] [58] [61] | [16] [21] [22] [40] [47] | [7] [16] [17] [19] [20] [23] [27] [43] [51] [52] [53] [54] [57] [61] [62] [64] | [56] | [35] | [28] [30] [32] [33] [34] [41] [50] [57] | [13] [23] [31] [39] | ||||
Raster width | [27] [61] | [15] [57] | [28] | [21] [22] [27] [40] [43] [48] [57] [61] | [17] [18] [19] | [23] [33] | [41] | |||||
Build orientation angle | [38] [44] [45] [61] | [14] [15] [16] [28] [37] | [57] [60] | [51] [61] | [16] [17] [18] [52] | [45] [57] [60] | [41] [57] | [13] [23] [33] [42] | ||||
Raster angle | [27] | [14] [28] | [18] | [17] [27] [36] [43] [52] [64] | [41] | [23] [32] [33] [57] | ||||||
Raster-to-raster air gap | [27] [28] [38] | [17] [18] [27] [40] | [36] | [41] | [23] | [28] [32] | ||||||
Infill density | [45] [46] | [16] [55] [57] | [45] | [16] [22] [47] [54] [57] [62] | [51] | [35] | [60] | [31] | [57] | |||
Printing speed (PS) | [29] | [15] | [55] [57] | [22] [47] [54] [58] | [19] [57] [59] [62] | [59] | [50] | |||||
Nozzle temperature | [46] [63] | [38] [61] | [57] | [22] [47] [63] | [20] [41] [49] [53] [54] [57] [58] [59] [61] | [56] [60] | [35] [59] | [57] | ||||
Number of contours (NC) | [57] | [23] [57] | [23] [31] | |||||||||
Contour width | [38] | [40] | [52] | [33] | [28] [41] |
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Positive (direct) if the increase of the process parameter results in a statistically significant improvement of the performance measure. This kind of relationship is marked by its arrangement in the respective sub-column featured by an upwards arrow.
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Negative (inverse) if the increase of the process parameter results in a significant worsening of the performance measure. This kind of relationship is marked by its arrangement in the respective sub-column featured by a downwards arrow.
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Neutral if the tested relationship was neither significantly positive nor negative. This kind of relationship is marked by its arrangement in the respective sub-column featured by a dash.
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LT is the most studied parameter according to Table 1. Its impact on performance measures and process speed is straightforward in many studies. LT is a good candidate for affecting geometric quality because of its recognized role in the staircase effect of 3D-printed parts, e.g., [65]. A few studies have already considered this parameter in relation to geometric accuracy, but PT was never considered contextually.
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PS is possibly relevant when the accurate deposition of material is requested. The magnitude of its influence on process speed has been surprisingly overlooked based on Table 1.
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Number of contours (NC) can be crucial when it comes to the accuracy of external surfaces. Its effect on process duration has emerged as marginal so far.
Name of the geometric deviations | Brief explanation |
---|---|
Flatness | Minimum distance between two parallel planes defining a region of space which entirely contains the reference surface. |
Cylindricity | Minimum (radial) distance between two coaxial cylinders defining a region of space which entirely contains the reference surface. |
Concentricity | Minimum diameter of a cylinder having its axis parallel to a datum that defines a region of space which entirely contains the axis of reference cylindrical surface. |
Surface parallelism | Minimum distance between two parallel planes (parallel to a datum) defining a region of space which entirely contains the reference surface. |
Surface perpendicularity | Minimum distance between two parallel planes (perpendicular to a datum) defining a region of space which entirely contains the reference surface. |
3 Materials and methods
3.1 Design of the part
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A cylinder at the base of the piece (C1).
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Two concentric holes with a cylindrical shape and different diameters (C2 and C3) that are theoretically concentric even with C1.
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Eight surfaces perpendicular to C1 (S1, S2, S3, S4, S5, S6, S7, S8) arranged as a regular octagon.
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Eight surfaces inclined at 30° with respect to S-surfaces (I1, I2, I3, I4, I5, I6, I7, I8).
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Two inclined (at 30° with respect to the C1–C3 axis), symmetric holes with a cylindrical shape (C4 and C5) respectively on the surfaces I1 and I5.
3.2 Printing process
Ultimaker 2 + specifications | |
---|---|
Printing technology | Fused deposition modelling (FDM) |
Printing bed size | 223 × 223 × 205 mm |
Nozzle diameter | 0.40 mm |
Material | PLA |
Filament diameter | 2.85 mm |
Print head | 1 (Swappable nozzle) |
Parameters | Layer thickness [mm] | Printing speed [mm/s] | Number of contours [#] |
---|---|---|---|
Low | 0.16 | 72 | 1 |
Medium | 0.20 | 90 | 2 |
High | 0.24 | 108 | 3 |
Test (part) | Layer thickness [mm] | Printing speed [mm/s] | Number of contours [#] | Printing time [min] |
---|---|---|---|---|
1 | 0.16 | 72 | 1 | 179 |
2 | 0.16 | 72 | 2 | 198 |
3 | 0.16 | 90 | 1 | 149 |
4 | 0.16 | 90 | 2 | 165 |
5 | 0.16 | 72 | 3 | 218 |
6 | 0.16 | 108 | 1 | 130 |
7 | 0.16 | 108 | 3 | 157 |
8 | 0.16 | 90 | 3 | 181 |
9 | 0.16 | 108 | 2 | 143 |
10 | 0.20 | 90 | 2 | 134 |
11 | 0.20 | 90 | 1 | 121 |
12 | 0.20 | 72 | 2 | 160 |
13 | 0.20 | 72 | 1 | 145 |
14 | 0.20 | 90 | 3 | 146 |
15 | 0.20 | 108 | 2 | 116 |
16 | 0.20 | 108 | 3 | 127 |
17 | 0.20 | 108 | 1 | 105 |
18 | 0.20 | 72 | 3 | 176 |
19 | 0.24 | 108 | 3 | 105 |
20 | 0.24 | 108 | 1 | 87 |
21 | 0.24 | 72 | 3 | 146 |
22 | 0.24 | 72 | 1 | 120 |
23 | 0.24 | 108 | 2 | 96 |
24 | 0.24 | 90 | 3 | 121 |
25 | 0.24 | 90 | 2 | 110 |
26 | 0.24 | 90 | 1 | 100 |
27 | 0.24 | 72 | 2 | 133 |
3.3 Measuring process
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Vertical surfaces are usually sufficiently described by 10 points each (surfaces S1 to S8).
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Inclined surfaces are usually sufficiently described by 15 points each (surfaces I1 to I8).
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Cylindrical features are sufficiently described by a minimum number of 12 points each to a maximum number of 36 points each, depending on their orientation and dimensions: hence, cylinders C4 and C5 were measured by acquiring 12 points each, cylinders C2 and C3 by acquiring 20 points each, and C1 by acquiring 36 points.
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Horizontal planes are commonly established by acquiring 10 points each (planes P1 to P3).
Geometric deviations | Name | Part feature | |
---|---|---|---|
Flatness | FLATP FLATS FLATI | P1–P3 S1–S8 I1–I8 | Table 21 Table 22 Table 23 |
Cylindricity | CYLC | C1–C5 | Table 24 |
Concentricity | CONCC1C2 CONCC1C3 CONCC2C3 | C1 with respect to C2 C1 with respect to C3 C2 with respect to C3 | Table 25 ‘’ ‘’ |
Surface parallelism | PARP1P2 PARP1P3 PARP2P3 PARS5S1 PARS6S2 PARS7S3 PARS8S4 | P1 with respect to P2 P1 with respect to P3 P2 with respect to P3 S5 with respect to S1 S6 with respect to S2 S7 with respect to S3 S8 with respect to S4 | Table 26 ,, ,, Table 27 ,, ,, ,, |
Surface perpendicularity | PERPS1P1 PERPS2P1 PERPS3P1 PERPS4P1 PERPS5P1 PERP6xP1 PERP7xP1 PERP8xP1 | S1 with respect to P1 S2 with respect to P1 S3 with respect to P1 S4 with respect to P1 S5 with respect to P1 S6 with respect to P1 S7 with respect to P1 S8 with respect to P1 | Table 28 ‘’ ‘’ ‘’ ‘’ ‘’ ‘’ ‘’ |
4 Results and discussion
4.1 Statistical analysis of geometric deviations data
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FLATP, FLATS, and FLATI are related to the flatness of horizontal surfaces P, vertical surfaces S, and inclined surfaces I respectively;
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CYLC represents the cylindricity;
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CONCCxCy indicates the concentricity of the circular feature x with respect to y;
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PARPxPy and PARSxSy describe the parallelism among horizontal surfaces Px and Py, and vertical surfaces Sx and Sy respectively;
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PERPSxP1 indicates the perpendicularity of the vertical surface Sx with respect to the horizontal surface P1.
4.1.1 Flatness of horizontal surfaces
Analysis of variance for flatness of horizontal surfaces P | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 1446.3 | 1414.3 | 707.1 | 3.68 | 0.033 |
PS | 2 | 194.6 | 115.6 | 57.8 | 0.30 | 0.742 |
NC | 2 | 438.5 | 439.5 | 219.8 | 1.14 | 0.328 |
LT × PS | 4 | 635.2 | 725.5 | 181.4 | 0.94 | 0.448 |
LT × NC | 4 | 702.5 | 698.4 | 174.6 | 0.91 | 0.467 |
PS × NC | 4 | 412.1 | 379.9 | 95.0 | 0.49 | 0.740 |
LT × ,PS × NC | 8 | 713.4 | 713.4 | 89.2 | 0.46 | 0.875 |
Error | 45 | 8652.6 | 8652.6 | 192.3 | ||
Total | 71 | 13,195.2 |
4.1.2 Flatness of vertical surfaces
Analysis of variance for flatness of vertical surfaces S | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 5693.2 | 5693.2 | 2846.6 | 22.99 | < 0.001 |
PS | 2 | 616.2 | 616.2 | 308.1 | 2.49 | 0.086 |
NC | 2 | 144,285.5 | 144,285.5 | 72,142.8 | 582.70 | < 0.001 |
LT × PS | 4 | 423.8 | 423.8 | 106.0 | 0.86 | 0.492 |
LT × NC | 4 | 773.4 | 773.4 | 193.4 | 1.56 | 0.186 |
PS × NC | 4 | 611.8 | 611.8 | 152.9 | 1.24 | 0.297 |
LT × PS × NC | 8 | 1586.2 | 1586.2 | 198.3 | 1.60 | 0.127 |
Error | 189 | 23,399.9 | 23,399.9 | 123.8 | ||
Total | 215 | 177,390.0 |
4.1.3 Flatness of inclined surfaces
Analysis of variance for flatness of inclined surfaces I | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 4939.3 | 6490.3 | 3245.1 | 13.95 | < 0.001 |
PS | 2 | 1808.4 | 1911.6 | 955.8 | 4.11 | 0.018 |
NC | 2 | 69,367.2 | 69,789.5 | 34,894.8 | 149.98 | < 0.001 |
LT × PS | 4 | 456.7 | 389.7 | 97.4 | 0.42 | 0.795 |
LT × NC | 4 | 2833.4 | 2774.2 | 693.5 | 2.98 | 0.021 |
PS × NC | 4 | 825.4 | 791.6 | 197.9 | 0.85 | 0.495 |
LT × PS × NC | 8 | 2816.8 | 2816.8 | 352.1 | 1.51 | 0.155 |
Error | 177 | 41,181 | 41,181 | 232.7 | ||
Total | 203 | 124,228.1 |
4.1.4 Cylindricity
Analysis of variance for cylindricity of all holes C1–C5 | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 2103 | 2103 | 1051 | 0.23 | 0.791 |
PS | 2 | 24,579 | 24,579 | 12,289 | 2.74 | 0.069 |
NC | 2 | 5869 | 5869 | 2934 | 0.66 | 0.521 |
LT × PS | 4 | 2280 | 2280 | 570 | 0.13 | 0.972 |
LT × NC | 4 | 281 | 281 | 70 | 0.02 | 1.000 |
PS × NC | 4 | 2994 | 2994 | 748 | 0.17 | 0.955 |
LT × PS × NC | 8 | 1015 | 1015 | 127 | 0.03 | 1.000 |
Error | 108 | 483,570 | 483,570 | 4478 | ||
Total | 134 | 522,691 |
Analysis of variance for cylindricity of vertical features C1–C3 | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 684.5 | 896.6 | 448.3 | 0.95 | 0.392 |
PS | 2 | 6259.6 | 6200.8 | 3100.4 | 6.60 | 0.003 |
NC | 2 | 13,455.5 | 13,738.4 | 6869.2 | 14.63 | < 0.001 |
LT × PS | 4 | 1641.6 | 1435.0 | 358.8 | 0.76 | 0.554 |
LT × NC | 4 | 215.4 | 255.5 | 63.9 | 0.14 | 0.968 |
PS × NC | 4 | 2078.2 | 1994.7 | 498.7 | 1.06 | 0.385 |
LT × PS × NC | 8 | 1850.9 | 1850.9 | 231.4 | 0.49 | 0.855 |
Error | 51 | 23,007.1 | 23,007.1 | 469.5 | ||
Total | 77 | 215,110.2 |
Analysis of variance for cylindricity of inclined features C4–C5 | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 1381.7 | 2499.2 | 1249.6 | 1.39 | 0.267 |
PS | 2 | 24,107.9 | 23,997.7 | 11,998.9 | 13.39 | < 0.001 |
NC | 2 | 5764.5 | 7305.9 | 3653.0 | 4.08 | 0.029 |
LT × PS | 4 | 766.8 | 682.7 | 170.7 | 0.19 | 0.941 |
LT × NC | 4 | 1272.0 | 2076.1 | 519.0 | 0.58 | 0.680 |
PS × NC | 4 | 2934.4 | 3248.4 | 812.1 | 0.91 | 0.475 |
LT × PS × NC | 8 | 2987.5 | 2987.5 | 373.4 | 0.42 | 0.900 |
Error | 25 | 22,401.6 | 22,401.6 | 896.1 | ||
Total | 51 | 61,616.5 |
4.1.5 Concentricity
Analysis of variance for concentricity of vertical holes C1–C3 | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 70,065 | 66,613 | 33,306 | 6.92 | 0.002 |
PS | 2 | 124,699 | 121,132 | 60,566 | 12.59 | < 0.001 |
NC | 2 | 25,183 | 25,356 | 12,678 | 2.64 | 0.082 |
LT × PS | 4 | 43,751 | 41,325 | 10,331 | 2.15 | 0.089 |
LT × NC | 4 | 2151 | 2130 | 533 | 0.11 | 0.978 |
PS × NC | 4 | 9756 | 8892 | 2223 | 0.46 | 0.763 |
LT × PS × NC | 8 | 23,371 | 23,371 | 2921 | 0.61 | 0.767 |
Error | 50 | 240,520 | 240,520 | 4810 | ||
Total | 76 | 539,496 |
4.1.6 Surface parallelism for horizontal surfaces
Analysis of variance for parallelism between horizontal surfaces P | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 10,945 | 7630 | 3815 | 3.79 | 0.030 |
PS | 2 | 4070 | 3437 | 1719 | 1.71 | 0.192 |
NC | 2 | 9773 | 8288 | 4144 | 4.12 | 0.023 |
LT × PS | 4 | 6740 | 7476 | 1869 | 1.86 | 0.134 |
LT × NC | 4 | 22,382 | 14,182 | 3546 | 3.52 | 0.014 |
PS × NC | 4 | 1838 | 2558 | 640 | 0.64 | 0.640 |
LT × PS × NC | 8 | 12,285 | 12,285 | 1536 | 1.53 | 0.174 |
Error | 46 | 46,273 | 46,273 | 1006 | ||
Total | 72 | 114,304 |
4.1.7 Surface parallelism for vertical surfaces
Analysis of variance for parallelism between vertical surfaces S | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 9131.2 | 8883.0 | 4441.5 | 7.73 | 0.001 |
PS | 2 | 5151.6 | 5059.4 | 2529.7 | 4.40 | 0.016 |
NC | 2 | 44,484.9 | 41,639.3 | 20,819.7 | 36.21 | < 0.001 |
LT × PS | 4 | 2306.0 | 2030.0 | 507.5 | 0.88 | 0.478 |
LT × NC | 4 | 2630.4 | 3106.4 | 776.6 | 1.35 | 0.259 |
PS × NC | 4 | 2086.5 | 2357.4 | 589.4 | 1.03 | 0.400 |
LT × PS × NC | 8 | 878.2 | 878.2 | 109.8 | 0.19 | 0.991 |
Error | 76 | 43,694.7 | 43,694.7 | 574.9 | ||
Total | 102 | 110,363.5 |
4.1.8 Surface perpendicularity
Analysis of variance for perpendicularity between vertical surfaces and P1 | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 7857.5 | 7972.2 | 3986.1 | 30.97 | < 0.001 |
PS | 2 | 1575.8 | 2023.5 | 1011.8 | 7.86 | 0.001 |
NC | 2 | 129,610 | 125,435 | 62,717.5 | 487.34 | < 0.001 |
LT × PS | 4 | 574 | 705.3 | 176.3 | 1.37 | 0.246 |
LT × NC | 4 | 1077.5 | 1207.4 | 301.8 | 2.35 | 0.056 |
PS × NC | 4 | 860.4 | 882.1 | 220.5 | 1.71 | 0.149 |
LT × PS × NC | 8 | 1649.7 | 1649.7 | 206.2 | 1.60 | 0.127 |
Error | 176 | 22,650.2 | 22,650.2 | 128.7 | ||
Total | 202 | 165,855.1 |
4.2 Regression analysis
Geometric deviation | emin [mm] | eMAX [mm] | e% |
---|---|---|---|
FLATP | 0.0001 | 0.0181 | 16 |
FLATS | 0.0013 | 0.0225 | 22 |
FLATI | 0.0002 | 0.0197 | 11 |
CYLCv | 0.0009 | 0.0257 | 5 |
CYLCi | 0.0001 | 0.0363 | 16 |
CONCCxCy | 0.0042 | 0.0870 | 11 |
PARPxPy | 0.0002 | 0.0962 | 23 |
PARSxSy | 0.0014 | 0.0414 | 14 |
PERPSxP1 | 0.0002 | 0.0210 | 16 |
4.3 Printing times
Analysis of variance for printing times | ||||||
---|---|---|---|---|---|---|
Source | DOF | Seq SS | Adj SS | Adj MS | F | p |
LT | 2 | 14,112.9 | 14,112.9 | 7056.4 | 339.80 | < 0.001 |
PS | 2 | 9433.6 | 9433.6 | 4716.8 | 227.13 | < 0.001 |
NC | 2 | 3226.9 | 3226.9 | 1613.4 | 77.69 | < 0.001 |
Error | 20 | 415.3 | 415.3 | 20.8 | ||
Total | 26 | 27,188.7 |
Test | e% | Test | e% | Test | e% |
---|---|---|---|---|---|
1 | 1.03 | 10 | 4.48 | 19 | 2.06 |
2 | 3.76 | 11 | 4.63 | 20 | 12.60 |
3 | 3.68 | 12 | 1.68 | 21 | 1.51 |
4 | 1.75 | 13 | 2.95 | 22 | 1.17 |
5 | 6.44 | 14 | 5.07 | 23 | 6.83 |
6 | 1.38 | 15 | 1.14 | 24 | 3.74 |
7 | 1.02 | 16 | 2.93 | 25 | 1.93 |
8 | 0.15 | 17 | 1.03 | 26 | 1.28 |
9 | 1.54 | 18 | 0.05 | 27 | 1.35 |
4.4 Effects of parameters on quality vs. printing time
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PP% is the normalized process parameter (LT, or PS, or NC),
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PPi is the value of the process parameter to be normalized,
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DT% is the normalized geometric deviation or time,
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DTmax is its maximum overall value, and
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DTi is the value to be normalized.
5 Conclusions
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The geometry and size of the part; here, it can be however hypothesized that the topology would affect process times more than the effects of process parameters on geometric accuracy.
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The material used (PLA).
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The 3D printing FDM device.